The Real Johnson–Wilson cohomology of CP∞CP∞

We completely compute the Real Johnson–Wilson cohomology of CP∞CP∞. Applying techniques from equivariant stable homotopy theory to the Bockstein spectral sequence, we produce permanent cycles and solve extension problems to give an explicit description of the ring ER(n)⁎(CP∞)ER(n)⁎(CP∞).